A behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and...

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A behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and randomly assigns them to three different groups that are assigned different levels of goal difficulty. The dependent variable is performance on a verbal-fluency task. Before the study each student is give a general-ability test, whose scores are used as the covariate. The data for this research scenario are given below. Conduct an analysis of covariance using these data and answer the following questions. Use an alpha = .05 for all statistical tests. The average verbal fluency score is 48.267. The average general ability score is 20.7. Group Verbal Fluency General Ability Group Verbal Fluency General Ability 1 42 16 2 50 20 1 40 16 2 62 23 1 48 19 2 60 24 1 55 24 2 48 21 1 45 20 2 47 20 1 51 22 3 46 20 1 47 20 3 47 21 1 38 23 3 43 19 1 46 20 3 54 26 1 45 18 3 49 21 2 51 25 3 44 25 2 50 18 3 53 24 2 45 17 3 52 23 2 52 19 3 42 18 2 47 17 3 49 22 1. Is the assumption of homogeneity of regression met for these data? What specific information did you use to come to this conclusion? (2 points) 2. Does the covariate, general ability, have a significant relationship to the dependent variable? What specific information did you use to come to this conclusion? (2 points) 3. Assuming that homogeneity of regression was met, are there differences in the mean verbal fluency of the three groups? What specific information did you use to come to this conclusion? (2 points) 4. Assuming you conclude that all three groups are not the same in verbal fluency, use a Bonferroni procedure to determine which of the groups differ. Conduct Cohen’s d standardized mean difference effect sizes for each of these pairwise differences. (4 points) 5. What proportion of variance in verbal fluency can be explained by the general ability and differences among the goal setting groups? What is the strength of association for the goal setting groups for participants that have the same general abilities? (4 points) 6. Write-up the results of your analysis in APA-format including a discussion of assumption testing, results of all statistical analyses, and effect size reporting (6 points).
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Answered 32 days AfterAug 25, 2021

Answer To: A behavioral psychologist is interested in whether goal-setting activities can be applied...

Suravi answered on Sep 26 2021
148 Votes
1. Homegeneity of regression means slope of both the variables are similar, they are homogeneous
H0 : There is no homogeneity of regression
H1 : There is homogeneity of regression
    Tests of Between-Subjects Effects
    Dependent Variable: Verbal_Fluency
    Source
    Type III Sum of Squares
    df
    Mean Square
    F
    Sig.
    Corrected Model
    416.510a
    5
    83.302
    4.908
    .003
    Intercept
    278.050
    1
    278.050
    16.382
    .000
    Group
    1.353
    2
    .676
    .040
    .961
    General_Ability
    253.610
    1
    253.610
    14.942
    .001
    Group * General_Ability
    5.314
    2
    2.657
    .157
    .856
    Error
    407.356
    24
    16.973
    
    
    Total
    70714.000
    30
    
    
    
    Corrected Total
    823.867
    29
    
    
    
    a. R Squared = .506 (Adjusted R Squared = .403)
From the table above we see sig level for Group*General Ability is 0.856 which is greater than 0.05 so we accept null hypothesis and conclude that the assumption of homogeneity of regression is met.
2.
Covariate General ability have significant relationship to the dependent variable verbal fluency with sig value being 0.001
    Tests of Between-Subjects Effects
    Dependent Variable: Verbal_Fluency
    Source
    Type III Sum of Squares
    df
    Mean Square
    F
    Sig.
    Corrected Model
    416.510a
    5
    83.302
    4.908
    .003
    Intercept
    278.050
    1
    278.050
    16.382
    .000
    Group
    1.353
    2
    .676
    .040
    .961
    General_Ability
    253.610
    1
    253.610
    14.942
    .001
    Group * General_Ability
    5.314
    2
    2.657
    .157
    .856
    Error
    407.356
    24
    16.973
    
    
    Total
    70714.000
    30
    
    
    
    Corrected Total
    823.867
    29
    
    
    
    a. R Squared = .506 (Adjusted R Squared = .403)

3.
The sig value for group is 0.062 thus there is significant difference in the mean of verbal fluency of the three group
    Descriptive Statistics
    Dependent Variable: Verbal_Fluency
    Group
    Mean
    Std. Deviation
    N
    1.00
    45.7000
    5.03433
    10
    2.00
    51.2000
    5.59365
    10
    3.00
    47.9000
    4.22821
    10
    Total
    48.2667
    5.33003
    30
    ANOVA
    Verbal_Fluency
    
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    Between Groups
    153.267
    2
    76.633
    3.085
    .062
    Within Groups
    670.600
    27
    24.837
    
    
    Total
    823.867
    29
    
    
    
4.
    Multiple Comparisons
    Dependent Variable: Verbal_Fluency
    Bonferroni
    (I) Group
    (J) Group
    Mean Difference (I-J)
    Std. Error
    Sig.
    95% Confidence Interval
    
    
    
    
    
    Lower Bound
    Upper Bound
    1.00
    2.00
    -5.50000
    2.22877
    .061
    -11.1888
    .1888
    
    3.00
    -2.20000
    2.22877
    .997
    -7.8888
    3.4888
    2.00
    1.00
    5.50000
    2.22877
    .061
    -.1888
    11.1888
    
    3.00
    3.30000
    2.22877
    .451
    -2.3888
    8.9888
    3.00
    1.00
    2.20000
    2.22877
    .997
    -3.4888
    7.8888
    
    2.00
    -3.30000
    2.22877
    .451
    -8.9888
    2.3888
Below is the Cohen’s d standardized mean difference effect sizes for each of these pairwise differences which was obtained by standardizing Verbal Fluency.
    Multiple Comparisons
    Dependent Variable: Zscore(Verbal_Fluency)
    Bonferroni
    (I) Group
    (J) Group
    Mean Difference (I-J)
    Std. Error
    Sig.
    95% Confidence Interval
    
    
    
    
    
    Lower Bound
    Upper Bound
    1.00
    2.00
    -1.03188957
    .41815320
    .061
    -2.0992084
    .0354292
    
    3.00
    -.41275583
    .41815320
    .997
    -1.4800746
    .6545630
    2.00
    1.00
    1.03188957
    .41815320
    .061
    -.0354292
    2.0992084
    
    3.00
    .61913374
    .41815320
    .451
    -.4481851
    1.6864526
    3.00
    1.00
    .41275583
    .41815320
    .997
    -.6545630
    1.4800746
    
    2.00
    -.61913374
    .41815320
    .451
    -1.6864526
    .4481851
5.
    Tests of Between-Subjects Effects
    Dependent Variable: Verbal_Fluency
    Source
    Type III Sum of...
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